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On stability of probability laws with univariate stable marginals

Summary

Examples of D. Marcus in ℝ2 dispel the belief that a probability measure on ℝd is stable if and only if all its univariate marginals are stable. However, in ℝd (in fact, in fairly general linear spaces), a probability measure whose two-dimensional marginals are all infinitely divisible is stable if and only if all its univariate marginals are stable.

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Partially supported by National Science Foundation Grant no MCS-81-00728.

Partially supported by National Science Foundation Grant no MCS-81-01895.

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Giné, E., Hahn, M.G. On stability of probability laws with univariate stable marginals. Z. Wahrscheinlichkeitstheorie verw Gebiete 64, 157–165 (1983). https://doi.org/10.1007/BF01844604

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Keywords

  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Linear Space
  • Mathematical Biology